The aim of this paper is to study the special functions known as Ihara Selberg zeta functions for Cayley graphs of finite Heisenberg groups as well as their factorizations into products of Artin-Ihara L-functions. The Heisenberg group H(R) over a ring R consists of upper triangular 3×3 matrices with entries in R and ones on the diagonal. The Ihara-Selberg zeta function is analogous to the Riemann zeta function with primes replaced by certain closed paths in a graph. This paper is a continuation of (DeDeo et al., 2004) where we presented a study of the statistics of the spectra of adjacency matrices of finite Heisenberg graphs.
with Martínez M., Medrano A., Minei M., Stark H., Terras A. (2005) Zeta Functions of Heisenberg Graphs over Finite Rings. In: Ismail
DOI: 10.1007/0-387-24233-3_8 MR2132463 05C25 (05C38 11M41 11R42 20H25)